Stability in Time-Delay Systems: Quiet Standing Case Study

The analysis of linear time-delay systems has attracted much interest in the literature over last five decade. Two types of stability conditions, namely delay-independent which results guarantee stability for arbitrarily large delays and delay-dependent, results take into account the maximum delay that can be tolerated by the system and, thus, are more useful in applications. The stability in general for linear time-delay systems, can be checked exactly only by eigenvalue considerations. When reasonable chosen with intentional delays, case study effects on time-delay of ankle torque on the stability of quiet standing, it can be used to stabilize and improve the close-loop response of these systems

H∞ Controller Design for Preview and Delayed Systems

The H∞ control problem of general preview/delayed systems is solved using analytic solutions of the corresponding operator Riccati equations. The solution to the problem can be applied to a broad range of input/output delayed systems and enables the handling of preview/delayed control problems. The solvability condition is characterized by the roots of the transcendental equations and the control law for the general problem is given based on a predictive compensation with an integro-differential observer. Some interpretations of typical control problems are presented based on the solvability condition and the resulting control law